Dynamical decoding of the competition between charge density waves in a kagome superconductor

TL;DR

This work addresses the competing twofold nature of $2\times2\times2$ CDW reconstructions in CsV$_3$Sb$_5$ by employing time-resolved X-ray diffraction with a near-infrared pump, revealing distinct, nonthermal melting and domain-size changes that demonstrate phase competition between the $MLL$ and $LLL$ CDW phases. A combined approach of structure-factor calculations and time-dependent Landau theory simulations links the observed differential peak dynamics to the respective susceptibilities of the two phases to photo-excitation, showing that the $L$-driven distortion is more quenched than the $M$-driven one, and that the more robust phase expands its domains at the expense of the other. The study provides a non-equilibrium framework to disentangle coexisting CDW reconstructions and suggests a mechanism—likely related to interlayer coupling—for the differing quenchabilities of $M$ and $L$. These insights advance understanding of intertwined charge orders and offer a generalizable approach for decoding phase competition in complex electronic systems using ultrafast diffraction.

Abstract

The kagome superconductor CsV$_3$Sb$_5$ hosts a variety of charge density wave (CDW) phases, which play a fundamental role in the formation of other exotic electronic instabilities. However, identifying the precise structure of these CDW phases and their intricate relationships remain the subject of intense debate, due to the lack of static probes that can distinguish the CDW phases with identical spatial periodicity. Here, we unveil the competition between two coexisting $2\times2\times2$ CDWs in CsV$_3$Sb$_5$ harnessing time-resolved X-ray diffraction. By analyzing the light-induced changes in the intensity of CDW superlattice peaks, we demonstrate the presence of both phases, each displaying a significantly different amount of melting upon excitation. The anomalous light-induced sharpening of peak width further shows that the phase that is more resistant to photo-excitation exhibits an increase in domain size at the expense of the other, thereby showcasing a hallmark of phase competition. Our results not only shed light on the interplay between the multiple CDW phases in CsV$_3$Sb$_5$, but also establish a non-equilibrium framework for comprehending complex phase relationships that are challenging to disentangle using static techniques.

Figures (20)

• Figure 1: Phase competition and CDW superlattice dynamics in CsV$_3$Sb$_5$.a,b Lattice distortions corresponding to the instabilities of phonons at $M$ (0.5 0 0) and $L$ (0.5 0 0.5) points in the momentum space. $M00$ ($L00$) corresponds to the case where the in-plane unit-cell doubling is along the $a$-axis and no doubling is present along the other two symmetry-equivalent directions, namely the $b$- and $(a+b)$-axes. c,d Two most probable $2\cross2\cross2$ CDW structures of CsV$_3$Sb$_5$. Note that in panels a-d, only the contracted bonds are colored in brown and only the V atoms are represented by the green balls for clarity. e, Schematic evolution of the two competing phases, $\Delta_1$ and $\Delta_2$, in the phase space. The red (green) arrow characterizes the change in the amplitude of $\Delta_{1 (2)}$, which is suppressed less (more) by light. Two insets show that phase competition leads to a suppression in order parameter amplitude and a change in real space domain size upon light excitation. f, Schematic of the near-infrared (NIR) pump and hard X-ray probe experimental setup (Methods). Time delay $t$ between the pump and probe can be varied. The sample is rotated nearly around its surface normal to fulfill the Bragg condition for a given diffraction peak. V atoms are represented by green balls while Sb atoms are represented by purple balls. Cs atoms are neglected in the crystal structure for clarity. Raw image of the (0 -1.5 2.5) superlattice peak before pumping is shown. The inset depicts the two-dimensional X-ray camera plane in the three-dimensional momentum space when measuring the peak at (0 -1.5 2.5). The two directions, $q_{\perp}$ and $q_{//}$, are nearly parallel to L and K directions, respectively. This holds true for the other peaks under investigation. g-i, Intensity linecuts $I$ integrated over the $q_{//}$ direction normalized by its equilibrium peak value at representative time delays. Solid lines are fits to Gaussians. Gray curves in panels h and i are the fitting curves reproduced from panel g for better comparison.
• Figure 2: Dynamics of the CDW peak intensity revealing the coexistence of the CDWs.a-c, Temporal evolution of the intensity $I$ obtained by tr-XRD measurements at $T$ = 30 K normalized to the static value for select pump fluences $F$ of CDW peaks at (0 -1.5 2.5), (-0.5 -1 2), and (0 -1.5 3), respectively. Solid lines in a are fits to a single damped oscillation atop a single exponential decay, while solid lines in b and c are fits to a single exponential decay (Methods). d-f, Temporal evolution of the normalized integrated intensity $I_{int}$ obtained by simulations based on a combination of time-dependent Landau theory (TDLT) and structural factor (SF) calculation (Methods). The disparity in penetration depths of the X-ray when measuring different peaks has been considered (Supplementary Information Section 13). Fluence ranges are identical for all three peaks. The order parameter governing each peak is shown at the top.
• Figure 3: Dynamics of the CDW peak width revealing the competition between the CDWs.a, Schematics of the differential peak-intensity-normalized linecuts along $q_{\perp}$, which are obtained by subtracting a broader Gaussian from a narrower Gaussian. b, Differential peak-intensity-normalized linecuts along $q_{\perp}$ acquired at $t=-1$ and $t=8$ ps of the peak at (0 -1.5 2.5). Solid lines are fits to zero constant and subtraction of two Gaussians, respectively. c,d, Temporal evolution of the (0 -1.5 2.5) peak width along $q_{//}$ and $q_{\perp}$ directions pumped at $F=0.25$ (light orange) and 2.5 mJ/cm$^2$ (dark red) normalized by their equilibrium values. Solid lines are fits to a single exponential decay. e, Schematics of the differential peak-intensity-normalized linecuts along $q_{\perp}$, which are obtained by subtracting a narrower Gaussian from a broader Gaussian. f-h, Same plots as panels b-d but for the peak at (0 -1.5 3). Lighter and darker green correspond to pumping at $F=0.25$ and 2.5 mJ/cm$^2$, respectively.
• Figure 4: Physical picture of the CDW dynamics in the presence of phase competition.a,b, Schematics of equilibrium and excited diffraction patterns of peaks arising from the $MLL$ and $LLL$ structures, respectively. The shallower color in the excited cases characterizes the lower peak intensity, while the change in peak dimensions characterizes the light modulation of peak width. Peak widths are inversely proportional to the correlation lengths as denoted. c,d, Schematics of equilibrium and excited real-space configuration of the $MLL$ and $LLL$ structures in and out of the kagome plane, respectively. Color code is the same as that used in panels a and b. Equilibrium and exited correlation lengths are denoted. The spatial inhomogeneity of light suppression, as reflected by the color gradient, suggests $MLL$ expands the most along both in-plane and out-of-plane directions near the sample surface.e,f,Schematics of free energy landscapes of the equilibrium and excited states in the phase space constructed by the $MLL$ and $LLL$ phases (Supplementary Information Section 11). Equilibrium and exited values of the order parameter amplitude corresponding to the two phases are denoted. Note that this figure represents the general case where $LLL$ near the surface is incompletely melted.
• Figure S1: Structure factor calculation results for CDW satellite peaks. Calculated (0 K L) CDW superlattice peak intensity map of a, the $MLL$ (and its symmetry-equivalent nematic domains $LML$, $LLM$) and b, the $LLL$ structures. The red and green circles denote the peaks at (0 -1.5 2.5) and (0 -1.5 3.0) studied in this work, respectively. We neglect the Bragg peaks for simplicity.